GREER, S.C. (AP) — Republican presidential contender Mitt Romney declared Thursday he has paid at least 13 percent of his income in federal taxes every year for the past decade, offering that new detail while still decrying a "small-minded" fascination over returns he will not release. President Barack Obama's campaign shot back in doubt: "Prove it."

Campaigning separately, Romney and running mate Paul Ryan also scrambled to explain their views on overhauling Medicare, the health care program relied on by millions of seniors.

Romney, the former company CEO, set up a whiteboard to make his case with a marker, while lawmaker Ryan resorted to congressional process language to explain why his budget plan includes the same $700 billion Medicare cut that he and Romney are assailing Obama for endorsing.

Essentially, Ryan said, he had to do it because Obama did it first.

Politically, both topics tie into major elements of the presidential race less than three months before the election: how well the candidates relate to the daily concerns and to the life circumstances of typical voters. Democrats are using the tax issue to raise doubts about Romney's trustworthiness — or, as Republicans contend, to distract from a weak economic recovery under Obama.

Romney's comments in South Carolina — at a news conference designed to focus on Medicare — showed that he remains sensitive to criticism of his tax payments but still is determined to release no more than two years of records despite contrary advice from some prominent Republicans.

The Obama campaign has aired an ad that, without evidence, raises the prospect that Romney paid no taxes some years. Senate Majority Leader Harry Reid, D-Nev., elevated that suggestion by claiming, also without proof, that an anonymous source told him Romney had not paid taxes for 10 years.

"I did go back and look at my taxes and over the past 10 years I never paid less than 13 percent," Romney told reporters after he landed in South Carolina for a fundraising event. "I think the most recent year is 13.6 or something like that. So I paid taxes every single year."

Aides later said Romney meant to say 13.9 percent, the amount he already disclosed for his 2010 federal return.

On average, middle income families, those making from $50,000 to $75,000 a year, pay 12.8 percent of their income in federal taxes, according to the nonpartisan Joint Committee on Taxation. In 2010 and 2011, Romney made about $21 million a year.

Romney is able to keep his tax rate low because most of his income is from investments, which are generally taxed at a lower rate than wages. That type of legal tax figuring is something Obama has proposed changing, although his campaign notably said nothing about Romney's self-described tax rate itself.

Instead, the campaign targeted only Romney's truthfulness, refusing to accept his answer and pressuring him to release years of earlier tax returns.

"Prove it," said Obama spokeswoman Lis Smith. "Given Mitt Romney's secrecy about his returns, coupled with the revelations in just the one return we have seen to date and the inconsistencies between this one return and his other financial disclosures, he has forfeited the right to have us take him just at his word."

Reid's office said much the same. Romney demanded that Reid "put up" the name of his anonymous source.

"Given the challenges that America faces — 23 million people out of work, Iran about to become nuclear, one out of six Americans in poverty — the fascination with taxes I've paid I find to be very small-minded," Romney said.

Obama and Vice President Joe Biden have released their returns for the years since 2000. The Obamas paid 20.5 percent in federal income taxes in 2011.

Ryan, meanwhile, found himself doing his own explaining.

He and Romney have launched a new strategy this week of criticizing Obama for taking more than $700 billion in Medicare funds to help pay for his health care overhaul. Yet those same cuts are in a House Republican budget blueprint authored by Ryan.

A reporter pressed him on the issue during a stop at a hot dog restaurant in Warren, Ohio.

His explanation was that the Medicare cuts were part of the existing baseline budget, including the Obama health care law he opposes.

"It gets a little wonky, but it was already in the baseline," Ryan said. "We would never have done it in the first place."

Romney hadn't scheduled any public events but put together a last-minute news conference to explain the differences between his Medicare plan and Obama's.

"Which of these two do you think is better?" Romney asked as he stood under a glaring sun at an airport.

Romney says Obama has cut $716 billion from the Medicare trust fund to pay for his national health care overhaul, weakening the program. Those cuts, mostly from health providers and insurance plans instead of directly from beneficiaries, would decrease the cost of the entitlement program over time and extend the life of the trust fund.

Ryan's budget would make those same cuts, though he would use the savings differently.

Romney — and Ryan, since joining the ticket — insist the cuts must be restored. That could make Medicare go bankrupt more quickly. But Romney says other parts of his plan, including giving fewer benefits to wealthier retirees, would keep Medicare solvent in the long term.

Independent groups say he has not supplied enough details to determine whether he would significantly shore up Medicare in years to come.

Democratic strategists and party officials say that while they still expect the race to stay close through the fall, they sense a slight shift in Obama's favor over the past two weeks. However, they expect Romney to get a boost following his party's convention and say a dismal economic report right before the election could pull votes his way.

Obama spent the day in White House meetings save for a stop at Democratic National Committee headquarters. Romney is devoting most of this week, and much of next week, to raising money in non-competitive states including Alabama, South Carolina, Massachusetts, New York, Texas, Louisiana and New Mexico.